Overpartition analogues for the generalized Rogers–Ramanujan identities of Bressoud

In the past two decades, there have been a lot of research centred around overpartitions, some of which concern overpartition analogues of Rogers–Ramanujan type identities. In this paper, we present Rogers–Ramanujan type overpartition identities by considering Bressoud's even moduli generalization of the Rogers–Ramanujan identity and its overpartition analogue of Chen, Sang and Shi given in 2015. We first introduce another overpartition function C¯_k,a(n) and show that C¯_k,a(n) equals the overpartition function B¯_k,a,0(n) of Chen, Sang and Shi. Next, we study parity constrains on parts of overpartitions. Recently, Sang, Shi and Yee obtained Rogers–Ramanujan type identities for overpartitions by adding some parity constraints to even or odd parts of overpartitions Chen, Sang and Shi introduced in 2013. We make some modifications and add constraints to even or odd parts of overpartitions counted by C¯_k,a(n) and B¯_k,a,0(n) obtaining further Rogers–Ramanujan type overpartition identities.